question_answer

Find the horse power of engine used to fill a tank of size\[\text{1m}\times \text{2m}\times \text{1m}\] situated at an average height of 20 m with water from a well of depth 17. 3 m in 5 minutes. Assume 20% power is wasted.

Answer:

Volume of water to be lifted\[=1\times 2\times 1=2{{m}^{3}}\] Mass of water = 2000 kg Total height\[=(20+17.3)=37.3\,m\] Time\[=5\times 60\,s\] Power = ? We know that, \[Power\frac{Work\,\,done}{time}=\frac{2000\times 9.8\times 37.3}{5\times 60\times 746}[\because 746W=1HP]\] \[=\frac{9.8}{3}\] As 20 % of power is wasted, the useful power is 80 % \[\therefore \]The horse power of engine\[=\frac{9.8}{3}\times \frac{100}{80}=4.08\,\,HP\]